Bear in mind that there are people on these planets prior to colonization. The local militia you cheerfully demolish in order to colonize a planet is not just guarding an empty world -- there are independent civilians down there before you send colonists. Since the Vasari and Advent invaded Trader space, we can assume that these planets are home to independent Trader civilizations who haven't yet gotten the memo to join the Coalition. Presumably, when colonization occurs, the TEC gives them membership benefits (including tax breaks, Costco cards for everyone, and a nice fleet to defend them from the Advent and the Vasari), the Advent converts the locals to Unity worship, and the Vasari tell them to become valued citizens or die.
The way I see it, cultural overthrow means local insurrection, Heinlein-style (not that I agree with Heinlein on a lot of things, just saying): people buy the incoming propaganda, stage a revolution, overthrow the planetary capital, and establish a regime that is neutral with regard to both the original owner and your empire. Picture violence in the streets, tanks surrounding the capitol building, people with guns and rebel insignias standing on street corners, back-room debates about Marx, hidden weapons caches, that sort of thing.
Also, what Juletron said: population reflects taxable population. There are still people there, even after orbital bombardment, but they don't occupy cities and they don't take kindly to taxation.
To make a long story short, I'm pretty sure a planet overthrown by culture reverts to the independent state it maintained before anyone colonized it -- people living their lives until someone comes along and makes them an offer they don't refuse.